Like the Trinity broshure, the Watchtower article reproduced above only tells half the story. Yes, you do not find the Trinity doctrine spelled out or even presumed in NT and early patristic sources. As the sources presented by Amazing1914 and I show (particularly Athenagorus, Irenaeus, Tertullian, and Clement of Alexandria), it is not until the second half of the second century where you find statements expressing explicit trinitarian (or even full-blown binitarian) ideas. But what the Society downplays are christological and theological statements in early texts that do represent component notions of trinitarian theology, such as the Deity of Christ, the unity or equality of the Father and Son, the triadic description of the functions of the Father, Son, and Holy Spirit, the personhood of the Holy Spirit, etc. In short, we may not find the synthesis of the trinity in such early sources, but we do find many statements and views that cannot be made to agree with Watchtower theology.
To quote what they say on Ignatius:
Even if Ignatius had said that the Son was equal to the Father in eternity, power, position, and wisdom, it would still not be a Trinity, for nowhere did he say that the holy spirit was equal to God in those ways.
No, but that would still be significant and worthy of note because the Society does NOT claim that "the Son is equal to the Father in eternity, power, position, and wisdom", etc. By reducing the issue down to just "Does Ignatius mention the Trinity: Yes or No?", the Society can side step the things that Ignatius does say that conflicts with Watchtower theology.
But Ignatius did not say that the Son was equal to God the Father in such ways or in any other. Instead, he showed that the Son is in subjection to the One who is superior, Almighty God.
Even the Trinity doctrine in most its forms contends that Jesus can be "in subjection" to the Father in function and position, not in being or nature (as subordinationists hold), particularly in his earthly incarnation. The Society very rarely mentions this distinction. An earlier writer, Tertullian, subscribed to an economical trinity, so the Son and the Holy Spirit were subject to the Father and both derived from the Father, but this does not mean that he was not a trinitarian because he also claimed that these three persons together comprise God (rather, he did not subscribe to the later Nicene trinity). So stating that the Son is subject to the Father does not preclude trinitarianism as a whole. As for Ignatius, he described Jesus as subject to the Father in his incarnation ("Jesus Christ in the flesh was subject to the Father and the apostles were subject to Christ and the Father," Magnesians 13:2), and in role ("All of you follow the bishop as Jesus Christ follows the Father," Smyrnaeans 8:1), not in nature. These statements anticipate the later view of Tertullian...
Ignatius calls Almighty God “the only true God, the unbegotten and unapproachable, the Lord of all, the Father and Begetter of the only-begotten Son,” showing the distinction between God and His Son.
Every trinitarian believes that there is a "distinction between God and his Son", without it one has a modalism rejected as heretical by the church fathers. The Society often acts as if statements distinguishing the Son and the Father problematize trinitarian theologies when they do not. In point of fact, Ignatius veered pretty close on occasion to modalism; in Smyrnaeans 2:2, he states that Jesus "truly raised himself from the dead," whereas most writers said that God raised him from the dead. This is not to say that he was necessarily a modalist; the language rather indicates that Ignatius was not precise in his thinking and wording in the way later writers were. His theology was dominated by the view that Jesus Christ is the visible manifestation of God (Magnesians 8:2).
Ignatius shows that the Son was not eternal as a person but was created, for he has the Son saying: “The Lord [Almighty God] created Me, the beginning of His ways.” Similarly, Ignatius said: "There is one God of the universe, the Father of Christ, 'of whom are all things;' and one Lord Jesus Christ, our Lord, `by whom are all things.' "
LOL, these are actually two citations from the spurious epistles to the Tarsians and the Philippians, these were NOT written by Ignatius. So bringing them up is only to muddy the waters.
True, Ignatius calls the Son “God the Word.” But using the word “God” for the Son does not necessarily mean equality with Almighty God. The Bible also calls the Son “God” at Isaiah 9:6. John 1:18 calls the Son “the only-begotten god.” Being vested with power and authority from Jehovah God, the Father, the Son could properly be termed a “mighty one,” which is what “god” basically means.—Matthew 28:18; 1 Corinthians 8:6; Hebrews 1:2.
First of all, this statement does not hint at the remarkable frequency with which Ignatius referred to Jesus as God (theos). Second, limiting the meaning of theos to just "mighty one" is a case of special pleading; why not say that the Father is only "a mighty one" as well? Should we refer to the Father as "a god" rather than "God"? What's good for the goose is good for the gander. While the Society uses the anarthrous status of theos in John 1:1, 1:18 to argue that it means "a god" rather than "God," Ignatius in several places used articular theos to refer to Jesus. Thus, he said that "our God (ho theos), Jesus the Christ, was conceived by Mary" (Ephesians 18:2). He referred to Jesus in his incarnation as truly "God in man" (en anthrópó theos), a phrase that anticipates later two-natures theology but which also coheres to the divine-Christ-in-human-Jesus theology attested quite early (Ephesians 7:2). He referred to the "blood of God" (Ephesians 1:1) and "the suffering/passion of God" (Romans 6:3). Finally, he also referred to Jesus, "who for our sake became visible ... who for our sake endured suffering" as being "above time" (huper kairon) and "eternal/timeless (akhronon) and invisible" (Polycarp 3:2), a remarkable statement ignored by the Society and which by itself can suggest a co-eternity of the Son and Father (since the Father is also eternal, cf. 1 Timothy 1:17, which refers to "God" as eternal and invisble). Why the silence about these statements? Why does the Society quote a spurious statement about Christ being "created" which was not written by Ignatius, yet ignore a statement of Ignatius that referred to Christ as timeless/eternal, invisible, and impassible....language highly suggestive of Deity (cf. Romans 1:20, Colossians 1:15, 1 Timothy 1:17, etc.). The joint timelessness of the Son with the Father is also suggested in Magnesians 6:1: "Jesus Christ, who before the ages (hos pro aiónón) was with the Father," a wording that evokes John 1:1-2.